Marc G. Genton

Pratik Nag, Yiping Hong, Sameh Abdulah et al.

Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Matérn covariance is challenging. Previous studies in the literature have tackled this challenge by employing spatial partitioning techniques to estimate the parameters that vary spatially in the covariance function. The selection of partitions is an important consideration, but it is often subjective and lacks a data-driven approach. To address this issue, in this study, we utilize the power of Convolutional Neural Networks (ConvNets) to derive subregions from the nonstationary data. We employ a selection mechanism to identify subregions that exhibit similar behavior to stationary fields. In order to distinguish between stationary and nonstationary random fields, we conducted training on ConvNet using various simulated data. These simulations are generated from Gaussian processes with Matérn covariance models under a wide range of parameter settings, ensuring adequate representation of both stationary and nonstationary spatial data. We assess the performance of the proposed method with synthetic and real datasets at a large scale. The results revealed enhanced accuracy in parameter estimations when relying on ConvNet-based partition compared to traditional user-defined approaches.

Qilong Pan, Sameh Abdulah, Mustafa Abduljabbar et al.

Emulating computationally intensive scientific simulations is crucial for enabling uncertainty quantification, optimization, and informed decision-making at scale. Gaussian Processes (GPs) offer a flexible and data-efficient foundation for statistical emulation, but their poor scalability limits applicability to large datasets. We introduce the Scaled Block Vecchia (SBV) algorithm for distributed GPU-based systems. SBV integrates the Scaled Vecchia approach for anisotropic input scaling with the Block Vecchia (BV) method to reduce computational and memory complexity while leveraging GPU acceleration techniques for efficient linear algebra operations. To the best of our knowledge, this is the first distributed implementation of any Vecchia-based GP variant. Our implementation employs MPI for inter-node parallelism and the MAGMA library for GPU-accelerated batched matrix computations. We demonstrate the scalability and efficiency of the proposed algorithm through experiments on synthetic and real-world workloads, including a 50M point simulation from a respiratory disease model. SBV achieves near-linear scalability on up to 512 A100 and GH200 GPUs, handles 2.56B points, and reduces energy use relative to exact GP solvers, establishing SBV as a scalable and energy-efficient framework for emulating large-scale scientific models on GPU-based distributed systems.

Zuzheng Wang, Fouzi Harrou, Ying Sun et al.

Detecting anomalies in crowded video scenes is critical for public safety, enabling timely identification of potential threats. This study explores video anomaly detection within a Functional Data Analysis framework, focusing on the application of the Magnitude-Shape (MS) Plot. Autoencoders are used to learn and reconstruct normal behavioral patterns from anomaly-free training data, resulting in low reconstruction errors for normal frames and higher errors for frames with potential anomalies. The reconstruction error matrix for each frame is treated as multivariate functional data, with the MS-Plot applied to analyze both magnitude and shape deviations, enhancing the accuracy of anomaly detection. Using its capacity to evaluate the magnitude and shape of deviations, the MS-Plot offers a statistically principled and interpretable framework for anomaly detection. The proposed methodology is evaluated on two widely used benchmark datasets, UCSD Ped2 and CUHK Avenue, demonstrating promising performance. It performs better than traditional univariate functional detectors (e.g., FBPlot, TVDMSS, Extremal Depth, and Outliergram) and several state-of-the-art methods. These results highlight the potential of the MS-Plot-based framework for effective anomaly detection in crowded video scenes.

Jianwei Shi, Sameh Abdulah, Ying Sun et al.

Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by vulnerabilities such as single-point failures and communication bottlenecks. This paper presents a decentralized framework tailored for parameter inference in spatial low-rank models to address these challenges. A key obstacle arises from the spatial dependence among observations, which prevents the log-likelihood from being expressed as a summation-a critical requirement for decentralized optimization approaches. To overcome this challenge, we propose a novel objective function leveraging the evidence lower bound, which facilitates the use of decentralized optimization techniques. Our approach employs a block descent method integrated with multi-consensus and dynamic consensus averaging for effective parameter optimization. We prove the convexity of the new objective function in the vicinity of the true parameters, ensuring the convergence of the proposed method. Additionally, we present the first theoretical results establishing the consistency and asymptotic normality of the estimator within the context of spatial low-rank models. Extensive simulations and real-world data experiments corroborate these theoretical findings, showcasing the robustness and scalability of the framework.

Jianwei Shi, Sameh Abdulah, Ying Sun et al.

Spatial data are central to applications such as environmental monitoring and urban planning, but are often distributed across devices where privacy and communication constraints limit direct sharing. Federated modeling offers a practical solution that preserves data privacy while enabling global modeling across distributed data sources. For instance, environmental sensor networks are privacy- and bandwidth-constrained, motivating federated spatial modeling that shares only privacy-preserving summaries to produce timely, high-resolution pollution maps without centralizing raw data. However, existing federated modeling approaches either ignore spatial dependence or rely on synchronous updates that suffer from stragglers in heterogeneous environments. This work proposes an asynchronous federated modeling framework for spatial data based on low-rank Gaussian process approximations. The method employs block-wise optimization and introduces strategies for gradient correction, adaptive aggregation, and stabilized updates. We establish linear convergence with explicit dependence on staleness, a result of standalone theoretical significance. Moreover, numerical experiments demonstrate that the asynchronous algorithm achieves synchronous performance under balanced resource allocation and significantly outperforms it in heterogeneous settings, showcasing superior robustness and scalability.

Kesen Wang, Minwoo Kim, Stefano Castruccio et al.

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modeling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behavior is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model.

Kesen Wang, Marc G. Genton

In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. To address the limitations of the Gaussian models, a variety of skewed models has been proposed, of which the popularity has grown rapidly. These skewed models introduce parameters that govern skewness and tail weight. Among various proposals in the literature, unified skewed distributions, such as the Unified Skew-Normal (SUN), have received considerable attention. In this work, we revisit a more concise and intepretable re-parameterization of the SUN distribution and apply the distribution to random fields by constructing a generalized unified skew-normal (GSUN) spatial process. We demonstrate that the GSUN is a valid spatial process by showing its vanishing correlation in large distances and provide the corresponding spatial interpolation method. In addition, we develop an inference mechanism for the GSUN process using the concept of neural Bayes estimators with deep graphical attention networks (GATs) and encoder transformer. We show the superiority of our proposed estimator over the conventional CNN-based architectures regarding stability and accuracy by means of a simulation study and application to Pb-contaminated soil data. Furthermore, we show that the GSUN process is different from the conventional Gaussian processes and Tukey g-and-h processes, through the probability integral transform (PIT).

Jian Cao, Joseph Guinness, Marc G. Genton et al.

Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that are related to the response. For this setting, we propose a novel, scalable algorithm, coined VGPR, which optimizes a penalized GP log-likelihood based on the Vecchia GP approximation, an ordered conditional approximation from spatial statistics that implies a sparse Cholesky factor of the precision matrix. We traverse the regularization path from strong to weak penalization, sequentially adding candidate covariates based on the gradient of the log-likelihood and deselecting irrelevant covariates via a new quadratic constrained coordinate descent algorithm. We propose Vecchia-based mini-batch subsampling, which provides unbiased gradient estimators. The resulting procedure is scalable to millions of responses and thousands of covariates. Theoretical analysis and numerical studies demonstrate the improved scalability and accuracy relative to existing methods.